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A329704
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Numbers k such that the sum of divisors of k (A000203) and the sum of proper divisors of k (A001065) are both triangular numbers (A000217).
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1
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1, 2, 5, 36, 54, 441, 473, 6525, 52577, 124025, 683820, 1513754, 1920552, 6079931, 6762923, 14751657, 17052782, 17310942, 36543714, 49919939, 60260967, 251849052, 364535720, 372476909, 562047389, 670395564, 670440852, 783856979, 824626800, 1084201689, 1122603809
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OFFSET
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1,2
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COMMENTS
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Are 1 and 36 the only terms that are also triangular numbers?
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LINKS
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EXAMPLE
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5 is a term since sigma(5) = 6 and sigma(5) - 5 = 1 are both triangular numbers.
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MATHEMATICA
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triQ[n_] := IntegerQ @ Sqrt[8*n+1]; Select[Range[10^5], triQ[(s = DivisorSigma[1, #])] && triQ[s - #] &]
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PROG
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(PARI) isok(k) = my(s=sigma(k)); ispolygonal(s, 3) && ispolygonal(s-k, 3); \\ Michel Marcus, Feb 29 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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